Melting and critical superheating

Two mechanisms of melting are known, heterogeneous, where melting starts at surfaces, and homogeneous, where the liquid nucleates in the bulk crystal. If melting occurs homogeneously, a crystal can be superheated significantly above its melting temperature (T-m). At present, the physical meaning of the limit of superheating (T-LS) is unknown. We demonstrate, by molecular dynamics simulations, that the total energy of a solid at T-LS is equal to the total energy of its liquid at T-m at the same volume. In the high pressure limit T-LS and T-m are connected by the constant k(AB)=ln 2/3 via the relation k(AB)=T-LS/T-m-1.